This is an announcement for the paper "Note on distortion and Bourgain $\ell_1$ index" by Anna Maria Pelczar.

Abstract: The relation between different notions measuring proximity to $\ell_1$ and distortability of a Banach space is studied. The main result states that a Banach space, whose all subspaces have Bourgain $\ell_1$ index greater than $\omega^\alpha$, $\alpha<\omega_1$, contains either an arbitrary distortable subspace or an $\ell_1^\alpha$-asymptotic subspace.

Archive classification: math.FA

Mathematics Subject Classification: 46B20 (primary), 46B03 (secondary)

Remarks: 10 pages

The source file(s), distortion_bourgain.tex: 36771 bytes, is(are) stored in gzipped form as 0709.2272.gz with size 11kb. The corresponding postcript file has gzipped size 92kb.

Submitted from: anna.pelczar@im.uj.edu.pl

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http://front.math.ucdavis.edu/0709.2272

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http://arXiv.org/abs/0709.2272

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